Go Zendo

[yebellz]

[Vsotvep]

[Vsotvep]

Rule guess: Both Black and White have three stones that form an acute triangle.

[yebellz]

278 is red, but the rule guess is correct!

[yebellz]

@antonTobi

it could be a pain to check manually for messy boards!

I’m glad that someone got it before we got to messy board guesses

[antonTobi]

Wow yeah, acute seems possibly even more annoying to check

Some rules that would be really tedious with lots of stones could become very nice games with some restriction such as “koans must have no more than 10 stones”.

And more specific restrictions like “koans must have exactly 3 black and 3 white stones” could allow for some very creative rules while also helping the players a bit by making the huge search space more manageable.

[yebellz]

I think it would be annoying in the worst-case, that is confirming the non-existence of any acute triangles when there are many stones, and hence potential triangles, to check.

However, I think that such hard cases are perhaps a bit unlikely to naturally arise, unless someone maybe deliberately crafted an evil example. I guess that with many stones on the board, acute triangles are likely to exist and in most cases it is easy to quickly eyeball them to confirm their acuteness.

How would one craft some examples where it would be annoying to confirm the non-existence of acute triangles?

[richyfourtytwo]

Makes me wonder if any mathematician has ever strictly defined the attribute ‘annoying’ for something.

[ArsenLapin1]

@yebellz

How would one craft some examples where it would be annoying to confirm the non-existence of acute triangles?

Have a very very very large board. Draw two lines on that board, close to each other, almost parallel, but slightly diverging. Add many stones in the narrow area between the two lines.

Since there are many stones, there will be many triangles. But because the area between the two lines is narrow enough, it’s easy for the builder to ensure that none of the triangles are acute: if three stones are inside the same narrow band, and at least one of the stones is far enough from the other two, then the triangle has to be obtuse. However, the builder can space the stones just close enough that some triangles are just barely not acute, so that it is annoying to confirm that all triangles are non-acute.

Although, confirming that all triangles are non-acute will take at most linear time for this configuration, and by linear I mean you just have to follow the narrow band and look at the smallest triangle (the larger triangle are obviously “more obtuse” than the smaller ones). So it’s not that annoying after all.

[martin3141]

@ArsenLapin1

if three stones are inside the same narrow band, and at least one of the stones is far enough from the other two, then the triangle has to be obtuse.

An acute triangle can be very thin, so I think this is false as a stand-alone statement. But I believe it can be fixed, in the context of your construction, by positioning the two close points correctly with respect to the band.

Basically, the picture is points following a line in a zig-zag pattern with angles > 90°, right?

[martin3141]

@Vsotvep do you want to host the next game?

[Vsotvep]

Sure!

Green Koan:

Red Koan:

---

Let’s play by the rules that only one rule guess is allowed, and that this has to be ‘unanimously agreed on’ by the students, meaning that all students who join the game agree that this is the rule that is guessed (so any student can veto, in favour of guessing more koans).

You can submit as many koans as you want.

[yebellz]

I want to test some simple contact property

[Vsotvep]

[antonTobi]

Let’s try something kind of inbetween the first red and green:

[Vsotvep]

[antonTobi]

Alrighty, so this seems like the natural next step:

[Vsotvep]

[antonTobi]

So, switching 2 stones in 312 turns it from red to green:

Let’s look for other small changes to 312 that might turn it green:

[yebellz]

My theory is that each color reaches every empty region